Use the Laws of Logarithms to combine the expression.

Question

Use the Laws of Logarithms to combine the expression.
4 log x − (1/3)log(x² + 1) + 5 log(x − 1)

Answer 1

Hi Jacob, so here how it goes,

                                                                                       Logarithmic Property

4logx - (1/3)log(x² + 1) + 5log(x - 1)                                 rlogx = logx^r

logx⁴ - log(x² + 1)^1/3 + log(x - 1)⁵                                   logM +logN = log MN, M=log(x² + 1)^1/3

                                                                                                                      N= log(x - 1)⁵

logx⁴ - log(x²+1)^1/3(x-1)⁵                                                logM - logN = log(M/N), M= logx⁴

                                                                                                                       N= log(x²+1)^1/3(x-1)⁵   

log( _____x⁴_________)

      log(x²+1)^1/3(x-1)⁵ 

 

Happy to help,

Shannon